Microelectromechanical gyroscope for sensing angular rate and method of sensing angular rate

ABSTRACT

A microelectromechanical gyroscope includes: a substrate; a stator sensing structure fixed to the substrate; a first mass elastically constrained to the substrate and movable with respect to the substrate in a first direction; a second mass elastically constrained to the first mass and movable with respect to the first mass in a second direction; and a third mass elastically constrained to the second mass and to the substrate and capacitively coupled to the stator sensing structure, the third mass being movable with respect to the substrate in the second direction and with respect to the second mass in the first direction.

BACKGROUND

Technical Field

The present disclosure relates to a microelectromechanical gyroscope forsensing angular rate and to a method of sensing angular rate.

Description of the Related Art

As is known, use of microelectromechanical systems (MEMS) isincreasingly widespread in various sectors of technology and has yieldedencouraging results especially in the production of inertial sensors,microintegrated gyroscopes, and electromechanical oscillators for a widerange of applications.

In particular, there exist various types of MEMS gyroscopes, which aredistinguished by their rather complex electromechanical structure and bythe operating mode, but are in any case based upon detection of Coriolisaccelerations. In MEMS gyroscopes of this type, a mass is elasticallyconstrained to a substrate or stator to be able to translate in adriving direction and a sensing direction that are mutuallyperpendicular. By a control device, the mass is set in oscillation at acontrolled frequency and amplitude in the driving direction.

When the gyroscope turns about an axis perpendicular to the drivingdirection and to the sensing direction at an angular rate, on account ofthe motion in the driving direction, the mass is subject to a Coriolisforce and moves in the sensing direction. The displacements of the massin the sensing direction are determined both by the angular rate and bythe velocity in the driving direction and may be transduced intoelectrical signals. For instance, the mass and the substrate may becapacitively coupled so that the capacitance depends upon the positionof the mass with respect to the substrate. The displacements of the massin the sensing direction may thus be detected in the form of electricalsignals modulated in amplitude in a way proportional to the angularrate, with carrier at the frequency of oscillation of the driving mass.Use of a demodulator makes it possible to obtain the modulating signalthus to derive the instantaneous angular rate.

In many cases, however, the acceleration signal that carries informationregarding the instantaneous angular rate also contains spuriouscomponents that are not determined by the Coriolis acceleration and thuspresent in the form of disturbance. Not infrequently, for example, thespurious components may depend upon constructional imperfections of themicromechanical part, due to the limits of precision and to theproduction process spread. Typically, the effective oscillatory motionof the driving mass, as a result of a defect in the elastic constraintsprovided between the mass and the substrate, may be misaligned withrespect to the direction expected theoretically. This type of defectcommonly causes a quadrature signal component, which adds to the usefulsignal due to rotation of the microstructure. Like the Coriolis force,in fact, the misalignment causes the mass to displace also in thesensing direction, instead of just in the driving direction, andproduces a variation of the capacitance between the mass and thesubstrate.

Obviously, the consequences are a degraded signal-to-noise ratio and analtered dynamic of the read interface, at the expense of the signal tobe read, to an extent that depends upon the degree of the defects.

BRIEF SUMMARY

One or more embodiments of the present disclosure are directed to amicroelectromechanical gyroscope and a method of sensing angular rates.

According to one embodiment of the present disclosure, amicroelectromechanical gyroscope includes a substrate and a statorsensing structure fixed to the substrate. The gyroscope further includesa first mass elastically coupled to the substrate and movable withrespect to the substrate in a first direction and a second masselastically coupled to the first mass and movable with respect to thefirst mass in a second direction. The gyroscope includes a third masselastically coupled to the second mass to enable movement in the firstdirection and elastically coupled to the substrate to enable movement inthe second direction, the third mass being capacitively coupled to thestator sensing structure.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS

For a better understanding of the disclosure, some embodiments thereofwill now be described, purely by way of non-limiting example and withreference to the attached drawings, wherein:

FIG. 1 is a simplified block diagram of a microelectromechanicalgyroscope according to an embodiment of the present disclosure;

FIG. 2 is a simplified top plan view of a portion of themicroelectromechanical gyroscope of FIG. 1;

FIG. 3 is a simplified top plan view of a portion of amicroelectromechanical gyroscope according to a different embodiment ofthe present disclosure; and

FIG. 4 is a simplified block diagram of an electronic systemincorporating a microelectromechanical gyroscope according to thepresent disclosure.

DETAILED DESCRIPTION

With reference to FIG. 1, a microelectromechanical gyroscope accordingto an embodiment of the present disclosure is designated as a whole bythe number 1 and comprises a substrate 2, a microstructure 3, a controldevice 4, and a read device 5. As explained in detail hereinafter, themicrostructure 3 comprises movable parts and parts that are fixed withrespect to the substrate 2. The control device 4 forms a control loopwith the microstructure 3 and is configured to keep movable parts of themicrostructure 3 in oscillation with respect to the substrate withcontrolled frequency and amplitude. For this purpose, the control device4 receives position signals S_(P) from the microstructure 3 and suppliesdriving signals S_(D) to the microstructure 3. The read device 5supplies output signals S_(OUT) as a function of the movement of themovable parts of the microstructure 3. The output signals S_(OUT)indicate an angular rate of the substrate 2 with respect to a gyroscopicaxis of rotation.

Illustrated in FIG. 2 are the substrate 2 and, in greater detail, themicrostructure 3 according to one embodiment. In particular, themicrostructure 3 comprises a driving mass 7, a transduction mass 8, anda movable sensing structure 10.

The driving mass 7 is elastically constrained to the substrate 2 and ismovable with respect to the substrate 2 in a driving direction D1. Inuse, the control device 4 keeps the driving mass 7 in oscillation in thedriving direction D1 about a resting position. For this purpose, thecontrol device 4 uses movable driving electrodes 12 a, fixed to thedriving mass 7, and stator driving electrodes 12 b, fixed to thesubstrate 2. The movable driving electrodes 12 a and the stator drivingelectrodes 12 b are capacitively coupled in comb-fingered configurationand are substantially parallel to the driving direction D1. The statordriving electrodes 12 b receive the driving signals S_(D) from thecontrol device 4 through electrical-connection lines (not illustratedfor reasons of simplicity). The oscillations of the driving mass 7define a signal carrier for the transduction chain of the gyroscope 1.

The elastic connection of the driving mass 7 to the substrate 2 isobtained by elastic suspension elements 11 or “flexures”, which areconfigured to enable oscillations of the driving mass 7 with respect tothe substrate 2 in the driving direction D1 and to prevent othermovements of the driving mass 7, in particular in a transductiondirection D2 perpendicular to the driving direction D1. Here and in whatfollows, the expression “prevent movements in a direction” and similarexpressions, both in reference to the driving direction D1 and inreference to the transduction direction D2 or in any other direction,are to be understood in the sense of substantially limiting themovements in said direction, compatibly with what is allowed by thetechnological and geometrical limits in definition of the constraints.It is thus not to be understood that the expressions referred to are incontradiction with the presence of possible spurious movements in theforbidden directions that may be at the origin of signals of disturbancewith respect to the carrier defined by the oscillations of the drivingmass, but these movements are only ideally prevented by the specificconfiguration of the flexible elements and constraints that arepractically rigid in these directions.

The transduction mass 8 is elastically constrained to the driving mass 7and is movable with respect to the driving mass in the transductiondirection D2.

The elastic connection of the transduction mass 8 to the driving mass 7is obtained by elastic suspension elements 13, which are configured toenable oscillations of the transduction mass 8 with respect to thedriving mass 7 in the transduction direction D2 and prevent otherrelative movements of the transduction mass 8 with respect to thedriving mass 7, in particular in the driving direction D1. With respectto the substrate 2, instead, the transduction mass 8 is movable both inthe transduction direction D2 and also in the driving direction D1 as aresult of the drawing action of the driving mass 7 and of the constraintimposed by the elastic suspension elements 13.

The movable sensing structure 10 comprises a frame 15 and a set ofmovable sensing electrodes 16 a, which are supported by the frame 15 andextend parallel to the driving direction D1. The frame 15 is elasticallyconstrained to the transduction mass 8 and to the substrate 2. Withrespect to the substrate 2, the frame 15 is movable in the transductiondirection D2. With respect to the transduction mass 8, the frame 15 ismovable in the driving direction D1.

Elastic connection of the frame 15 to the substrate 2 is obtained byelastic suspension elements 18, which are configured to enableoscillations of the frame 15 with respect to the substrate 2 in thetransduction direction D2 and prevent other movements of the frame 15with respect to the substrate 2, in particular in the driving directionD1.

The frame 15 is coupled to the transduction mass 8 by elastic connectionelements 20, which are configured to prevent relative movements betweenthe transduction mass 8 and the frame 15 in the transduction directionD2. The elastic connection elements 20 enable, instead, other relativemovements between the transduction mass 8 and the frame 15. Inparticular, translatory oscillations in the driving direction D1 androtary oscillations are allowed. Consequently, the movements of thetransduction mass 8 in the transduction direction D2 are transmittedsubstantially in a rigid way, whereas the translatory movements in thedriving direction and the rotary movements of the transduction mass areat least in part compensated by the elastic connection elements 20. Dueto the elastic connection elements 20, which enable displacementsbetween the frame 15 and the transduction mass 8 in the drivingdirection D1, the frame 15 may be constrained to the substrate 2 asalready described without cancelling out the useful displacementcomponents due to the Coriolis force that acts on the transduction mass8. This would not be possible with a simple rigid connection between thetransduction mass 8 and the movable sensing structure 10.

The movable sensing structure 10 is capacitively coupled to a statorsensing structure 30, which comprises stator sensing electrodes 16 bfixed to the substrate 2 and extending in the driving direction D1. Inparticular, the movable sensing electrodes 16 a and the stator sensingelectrodes 16 b are coupled according to a “parallel plate” scheme anddefine a capacitor with a capacitance variable as a function of theposition of the movable sensing structure 10 with respect to thesubstrate 2 in the transduction direction D2.

As mentioned, in use, the control device 4 keeps the driving mass 7 inoscillation in the driving direction D1 with controlled frequency andamplitude. The transduction mass 8 is drawn by the driving mass 7 in themotion in the driving direction D1 as a result of the connection by theelastic suspension elements 13, which enable relative motion between thedriving mass 7 and the transduction mass 8 only in the transductiondirection D2. When the substrate 2 turns about a gyroscopic axis Gperpendicular to the driving direction D1 and to the transductiondirection D2, the transduction mass 8 is subjected to a Coriolis forcein the transduction direction D2. The transduction mass 8 thusoscillates in the transduction direction 8 with an amplitude thatdepends upon the linear drawing velocity in the driving direction D1 andby the angular rate of the substrate 2 about the gyroscopic axis G. Aspurious displacement, caused by imperfections of the elastic suspensionelements 11, may be added to the displacement due to the Coriolis force.The component due to the spurious displacement varies at the samefrequency as that of the carrier, but is phase-shifted by 90° withrespect to the Coriolis forcing term because it depends upon theposition and not upon the velocity in the driving direction D1. Theoverall displacement of the transduction mass 8 in the transductiondirection D2 is transmitted to the movable sensing structure 10 as aresult of the elastic connection elements 20, which allow relativetranslatory motion only in the driving direction D1.

The effect of the imperfections of the constraints, in particular of theelastic suspension elements 11 that connect the driving mass 7 to thesubstrate 2 is, however, transferred to the movable sensing structure 10to an extent much smaller than the contribution due to the Coriolisforce. The contribution due to the defects of driving in thetransduction direction D2 is thus attenuated for the transduction mass 8and the sensing mass 10 both by the elastic suspension elements 13between the driving mass 7 and the transduction mass 8 and by theelastic suspension elements 18 between the movable sensing structure 10and the substrate 2, as well as by the elastic connection elements 20between the transduction mass 8 and the frame 15. In particular, theelastic connection elements 20 are able to attenuate also spuriousrotary movements, which are transmitted to the transduction mass 8 bythe driving mass 7 and are not completely compensated for by the elasticsuspension elements 13. Instead, the contribution due to the Coriolisforce in the transduction direction D2 arises directly from thetransduction mass 8 and is transmitted without appreciable attenuationby the elastic connection elements 20, which enable a substantiallyrigid coupling in the direction D2, and this contribution is affectedthe action of the elastic suspension elements 13 and of the elasticsuspension elements 18 and is consequently transmitted in anon-attenuated way on the sensing mass 10. The Coriolis force on thedriving mass 7 is, instead, completely balanced by the elasticsuspension elements 11.

The weight of the spurious contributions is thus attenuated with respectto that of the contributions useful for detection of the angular rate,and the signal-to-noise ratio is accordingly improved.

FIG. 3 illustrates a different embodiment of the disclosure. In thiscase, a microelectromechanical gyroscope 100 comprises a substrate 102and a microstructure 103, in addition to a control device and to a readdevice (not illustrated).

The microstructure 103 comprises two actuation masses 106, two drivingmasses 107, two transduction masses, and four movable sensing structures110, all arranged symmetrically about a central anchorage 109.

In detail, the actuation masses 106 are arranged symmetrically withrespect to the central anchorage 109 and are aligned in an actuationdirection. The actuation masses 106 are elastically coupled to thesubstrate 102 for oscillating in a fixed actuation direction. Connectionto the substrate 102 is obtained by elastic elements 111 for connectionto respective outer ends. The actuation masses 106 are further coupledtogether through elastic connection elements 112 and a bridge 113, whichis in turn connected to the central anchorage 109. The bridge 113 isdefined by a frame surrounding the central anchorage 109 and connectedthereto to be able to oscillate out of plane with respect to twoperpendicular axes.

The actuation masses 106 are provided with respective sets of movableactuation electrodes 115 a, which are capacitively coupled incomb-fingered configuration to stator actuation electrodes 115 b fixedto the substrate 2. The control device (not illustrated) uses themovable actuation electrodes 115 a and the stator actuation electrodes115 b for keeping the actuation masses 106 in oscillation with respectto the actuation direction with controlled frequency and amplitude and,for example, with a mutual phase shift.

The driving masses 107 are arranged symmetrically with respect to thecentral anchorage 109 and are aligned in a driving direction D1′perpendicular to the actuation direction. The driving masses 107 areelastically coupled to the substrate 102 and to the actuation masses 106for oscillating in the driving direction D1′. In particular, eachdriving mass 107 is coupled to both of the actuation masses 106 byrespective elastic suspension elements 117, which are configured toconvert the motion of the actuation masses 106 in the actuationdirection into motion of the driving masses 107 in the driving directionD1′. The mutually phase-shifted oscillatory motion of the actuationmasses 106 in the actuation direction causes a corresponding mutuallyphase-shifted oscillatory motion of the driving masses 107 in thedriving direction D1′.

The driving masses 107 are further coupled to the substrate 102 byelastic suspension elements 118 and to the bridge 113 by elasticconnection elements 120. The elastic suspension elements 118 and theelastic connection elements 120 are configured to prevent movements ofthe driving masses 107 transverse to the driving direction D1′.

Each transduction mass 108 is elastically coupled to a respective one ofthe driving masses 107 by elastic connection elements 121. Thetransduction masses 108 are arranged symmetrically with respect to thecentral anchorage 109. The elastic connection elements 121 areconfigured to enable relative movements of the transduction masses 108with respect to the driving masses 107 in a transduction direction D2′perpendicular to the driving direction D1′ and for preventing relativemovements of the transduction masses 108 with respect to the drivingmasses 107 in the driving direction D1′ (in one embodiment, thetransduction direction D2′ is parallel to the actuation direction).

Coupled to each transduction mass 108 are two respective movable sensingstructures 110 on opposite sides with respect to the transductiondirection D2′.

Each movable sensing structure 110 comprises a frame 115 and a set ofmovable sensing electrodes 126 a, which are supported by the respectiveframe 115. The frames 115 are elastically constrained to the respectivetransduction masses 108 and to the substrate 102 and are movable withrespect to the substrate 102 in the transduction direction D2′ and withrespect to the respective transduction masses 108 in the drivingdirection D1′.

Elastic connection of the frames 115 to the substrate 102 is obtained byelastic suspension elements 128, which are configured to enableoscillations of the frames 115 with respect to the substrate 102 in thetransduction direction D2′ and prevent movements of the frames 115 withrespect to the substrate 102 in the driving direction D1′.

Elastic connection of the frames 115 to the respective transductionmasses 108 is obtained by elastic suspension elements 129, which areconfigured to enable oscillations of the transduction masses 108 withrespect to the respective frames 115 in the driving direction D1′ andprevent relative movements between the frames 115 and the respectivetransduction masses 108 in the transduction direction D2′.

The movable sensing structures 110 are capacitively coupled torespective stator sensing structures 130, which comprise respective setsof stator sensing electrodes 126 b fixed to the substrate 102. Inparticular, the movable sensing electrodes 126 a and the stator sensingelectrodes 126 b are coupled according to a parallel-plate scheme anddefine a capacitor with capacitance variable as a function of theposition of the movable sensing structures 110 with respect to thesubstrate 102 in the transduction direction D2′.

In the embodiment described, the actuation masses 106 and the drivingmasses 107 may be constrained to the substrate 102 so that respectiveout-of-plane rotary movements are allowed. In practice, the elasticconnection elements of the actuation masses 106 and of the drivingmasses 107 may be configured to enable rotations about respective axesparallel to the driving direction D1′ (for the actuation masses 106) orto the transduction direction D2′ (for the driving masses 107). In thiscase, the actuation masses 106 and driving masses 107 may becapacitively coupled to electrodes (not illustrated) arranged onrespective portions of the substrate 102. This makes it possible toprovide multiaxial gyroscopes, which may detect rotations of thesubstrate 102 also with respect to axes parallel to the drivingdirection D1′ or to the transduction direction D2′ (in practice,parallel to the surface of the substrate 102).

Also in this case, the transduction masses 108 and the movable sensingstructures 110 are separated from the driving masses 107 and coupled forpenalizing transfer of the spurious movements (due to defects of theconstraints) to the sensing structures. In particular, the result isfavored by the elastic suspension elements 128 between the frames 115and the substrate 102 and by the elastic suspension elements 129 betweenthe transduction masses 108 and the respective frames 115.

Illustrated in FIG. 4 is a portion of an electronic system 200 accordingto an embodiment of the present disclosure. The system 200 incorporatesthe electromechanical transducer 1 and may be used in devices such as,for example, a laptop computer or tablet, possibly withwireless-connection capacity, a cellphone, a smartphone, a messagingdevice, a digital music player, a digital camera, or other devicesdesigned to process, store, transmit, or receive information. Inparticular, the electroacoustic transducer 1 may be used for performingfunctions of voice control, for example, in a motion-activated userinterface for computers or consoles for video games or in asatellite-navigation device.

The electronic system 200 may comprise a control unit 210, aninput/output (I/O) device 220 (for example, a keyboard or a screen), thegyroscope 100, a wireless interface 240, and a memory 260, of a volatileor nonvolatile type, coupled together through a bus 250. In oneembodiment, a battery 280 may be used for supplying the system 200. Itshould be noted that the scope of the present disclosure is not limitedto embodiments necessarily having one or all of the devices listed.

The control unit 210 may comprise, for example, one or moremicroprocessors, microcontrollers and the like.

The I/O device 220 may be used for generating a message. The system 200may use the wireless interface 240 for transmitting and receivingmessages to and from a wireless-communication network with aradiofrequency (RF) signal. Examples of wireless interface may comprisean antenna, a wireless transceiver, such as a dipole antenna, eventhough the scope of the present disclosure is not limited from thispoint of view. Furthermore, the I/O device 220 may supply a voltagerepresenting what is stored either in the form of digital output (ifdigital information has been stored) or in the form of analoginformation (if analog information has been stored).

Finally, it is evident that modifications and variations may be made tothe microelectromechanical gyroscope and to the method described,without thereby departing from the scope of the present disclosure.

The various embodiments described above can be combined to providefurther embodiments. These and other changes can be made to theembodiments in light of the above-detailed description. In general, inthe following claims, the terms used should not be construed to limitthe claims to the specific embodiments disclosed in the specificationand the claims, but should be construed to include all possibleembodiments along with the full scope of equivalents to which suchclaims are entitled. Accordingly, the claims are not limited by thedisclosure.

1. A microelectromechanical gyroscope comprising: a substrate; a statorsensing structure fixed to the substrate; a first mass elasticallycoupled to the substrate and movable with respect to the substrate in afirst direction; a second mass elastically coupled to the first mass andmovable with respect to the first mass in a second direction; and athird mass elastically coupled to the second mass in a manner thatenables movement of the third mass with respect to the second mass inthe first direction and elastically coupled to the substrate in a mannerthat enables movement of the third mass with respect to the substrate inthe second direction, the third mass being capacitively coupled to thestator sensing structure.
 2. The gyroscope according to claim 1,comprising first elastic elements between the substrate and the thirdmass, the first elastic elements being configured to enable the movementof the third mass with respect to the substrate in the second directionand prevent movements of the third mass with respect to the substrate inthe first direction.
 3. The gyroscope according to claim 2, comprisingsecond elastic elements between the third mass and the second mass, thesecond elastic elements being configured to enable the movement of thethird mass with respect to the second mass in the first direction andprevent movements of the third mass with respect to the second mass inthe second direction.
 4. The gyroscope according to claim 3, comprisingthird elastic elements between the substrate and the first mass, thethird elastic elements being configured to enable movement of the firstmass with respect to the substrate in the first direction and preventmovements of the first mass with respect to the substrate in the seconddirection.
 5. The gyroscope according to claim 4, comprising fourthelastic elements between the first mass and the second mass, the fourthelastic elements being configured to enable movement of the second masswith respect to the first mass in the second direction and preventmovements of the second mass with respect to the first mass in the firstdirection.
 6. The gyroscope according to claim 1, wherein the third massis coupled to the stator sensing structure so that a capacitance betweenthe third mass and the stator sensing structure is determined by aposition of the third mass with respect to the substrate.
 7. Thegyroscope according to claim 1, wherein: the third mass includes asupporting element elastically coupled to the second mass and a set ofmovable sensing electrodes; and the stator sensing structure includes aset of stator sensing electrodes fixed to the substrate and capacitivelycoupled to respective movable sensing electrodes.
 8. The gyroscopeaccording to claim 1, comprising: movable driving electrodes fixed tothe first mass; and stator driving electrodes fixed to the substrate andcapacitively coupled to respective movable driving electrodes.
 9. Thegyroscope according to claim 1, wherein the first mass is one of aplurality of first masses, each elastically coupled to the substrate,the first masses being arranged symmetrically with respect to a centralanchorage and aligned in the first direction.
 10. The gyroscopeaccording to claim 9, comprising a plurality of fourth masses, eachelastically coupled to the substrate, wherein: the fourth masses beingarranged symmetrically with respect to the central anchorage and alignedin an actuation direction perpendicular to the first direction; and eachfirst mass being coupled to each of the fourth masses by respectivefurther elastic suspension elements, each first mass being configured toconvert movements of the fourth masses in the actuation direction intomovements of the first masses in the first direction.
 11. The gyroscopeaccording to claim 10, wherein the first masses and the fourth massesare coupled to the central anchorage by a bridge defined by a framesurrounding the central anchorage and coupled to the central anchorage,the bridge being configured to oscillate out of plane.
 12. The gyroscopeaccording to claim 9, wherein the second mass is one of a plurality ofsecond masses, each elastically coupled to a respective one of the firstmasses and arranged symmetrically with respect to the central anchorage.13. The gyroscope according to claim 12, comprising, for each secondmass, two respective third masses are located on opposite sides withrespect to the second direction.
 14. The gyroscope according to claim 1,wherein the second direction is perpendicular to the first direction.15. An electronic system, comprising: a microelectromechanical gyroscopeincluding: a substrate; a stator sensing structure fixed to thesubstrate; a first mass elastically coupled to the substrate and movablewith respect to the substrate in a first direction; a second masselastically coupled to the first mass and movable with respect to thefirst mass in a second direction; first elastic elements coupled to thesecond mass; second elastic elements coupled to the substrate; and athird mass elastically coupled to the second mass by the first elasticelements to enable movement of the third mass in the first directionwhile preventing movements in the second direction, the third masselastically coupled to the substrate by the second elastic elements toenable movement in the second direction while preventing movements inthe first direction, the third mass being capacitively coupled to thestator sensing structure; and a control unit coupled to the gyroscope.16. The electronic system according to claim 15, wherein the electronicsystem is at least one of a laptop, tablet, cellphone, smartphone,messaging device, digital music player, and digital camera.
 17. Theelectronic system according to claim 15, wherein the first mass is oneof a plurality of first masses, each elastically coupled to thesubstrate, the plurality of first masses being arranged symmetricallywith respect to a central anchorage and aligned in the first direction.18. A method of sensing angular rates, the method comprising:oscillating a first mass, elastically coupled to a substrate, withrespect to the substrate in a first direction; sensing displacements ofa second mass in a second direction, the second mass being elasticallycoupled to the first mass and movable with respect to the first mass inthe second direction; and sensing displacements of a third masscapacitively coupled to a stator sensing structure on the substrate andelastically coupled to the second mass and to the substrate, the thirdmass being movable with respect to the substrate in the second directionand with respect to the second mass in the first direction.
 19. Themethod according to claim 18, wherein the third mass is elasticallycoupled to the second mass in a manner that enables movement in thefirst direction while restricting movement in the second direction andto the substrate in a manner that enables movement in the seconddirection while restricting movement in the first direction.
 20. Themethod according to claim 19, wherein sensing displacement of the secondmass includes sensing displacements of a plurality of second masses thatare movable with respect to the first mass in the second direction. 21.The method according to claim 18, wherein the second direction isperpendicular to the first direction.